TY  - JOUR
ID  - Almaslokh2023
LB  - Almaslokh2023
AU  - Almaslokh, Abdulaziz
AU  - Qian, Chuanxi
TI  - Global attractivity of a higher order nonlinear difference equation with unimodal terms
ST  - Global attractivity of a higher order nonlinear difference equation with unimodal terms
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2023
VL  - 43
IS  - 2
SP  - 131
EP  - 143
DO  - https://doi.org/10.7494/OpMath.2023.43.2.131
UR  - https://doi.org/10.7494/OpMath.2023.43.2.131
AB  - In the present paper, we study the asymptotic behavior of the following higher order nonlinear difference equation with unimodal terms \[x(n+1)= ax(n)+ bx(n)g(x(n)) + cx(n-k)g(x(n-k)), \quad n=0, 1, \ldots,\] where \(a\), \(b\) and \(c\) are constants with \(0\lt a\lt 1\), \(0\leq b\lt 1\), \(0\leq c \lt 1\) and \(a+b+c=1\), \(g\in C[[0, \infty), [0, \infty)]\) is decreasing, and \(k\) is a positive integer. We obtain some new sufficient conditions for the global attractivity of positive solutions of the equation. Applications to some population models are also given.
KW  - higher order difference equation
KW  - positive equilibrium
KW  - unimodal term
KW  - global attractivity
KW  - population model
SN  - 1232-9274
ER  -